Class 12th

Suppose that intensity of a laser is (315/π) W/m². The rms electric field, in units of V/m associated with this source is close to the nearest integer is (ε₀ = 8.86 * 10⁻¹² C²N⁻¹m⁻²; c = 3 * 10⁸ ms⁻¹)

An electron is moving along +x direction with a velocity of 6 * 10? ms?¹. It enters a region of uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be:

Identify the correct output signal Y in the given combination of gates (as shown) for the given inputs A and B.

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in metres) is [numerical value].

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m, BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is [numerical value].

A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:

If a and b are unit vectors, then the greatest value of √3|a+b|+|a-b| is [numerical value].

Let f:R→R be defined as f(x)={x⁵sin(1/x)+5x², x<0; 0, x=0; xcos(1/x)+x, x>0}. The value of λ for which f"(0) exists, is [numerical value].

You are given that Mass of ?Li = 7.0160u, Mass of ?He = 4.0026u and ¹H = 1.0079u. When 20 g of ?Li is converted into ?He by proton capture, the energy liberated, (in kWh), is [Mass of nucleon = 1GeV/c²]

Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is [numerical